Methodology

To calculate the exposure index \(E_{ij}\), we modelled the diffusion of theoretical particles in an ecosystem. Particles are the resultant of an activity, such as contaminants or sediment, and they diffuse from the source of the activity. Three types of particles have been considered, in order to use multiple sinking rates. Combination of the responses for each particle type will allow to represent each activity by a unique signature.

We simulated the dispersion of these particles using the minimal distance from the source \(D\) and an inverse logarithm relationship, to account for a ‘journey’ in a 2D environment while reducing the contribution of highest values.

The three types of particle considered were:

• slow-sinking particles (< 4 µm): e.g. clay, dissolved organic matter, small bacteria, viruses, chemical components, proteins
• medium-sinking particles (between 4 µm and 2 mm): e.g. sand, silt, small particulate organic matter, large bacteria, phytoplankton, zooplankton
• fast-sinking particles (> 2 mm): e.g. gravel, large particulate organic matter, clusters of dead organisms, large zooplankton, larger organisms

\(D_{ijk}\) has been calculated with least-cost pathfinding methods from the package gdistance. To compute the trajectory of each particles type, we first established a connectivity model based on a ‘resistance seascape’ concept. We created a 100 x 100 m raster in our study area, whose cell can be selected to obtain the path connecting start (source of the activity) and end (raster cell) points. Journey between two neighbour cells (chess queen configuration) has a cost to be included in this path, which is defined on several constraints to account for specific behaviour. The length of the final path then gives the distance.

We considered four underlying principles for the physical constraints:

• marine ecosystems: particles cannot disperse on land
• gravity: particles disperse easily from shallow to deeper depths while the reverse is difficult
• sedimentation: particles cannot disperse anymore when they have sedimented
• hydrodynamism: particles disperse according to local hydrodynamical currents

⚠️ For now, the forth constraint is not yet implemented.

The connectivity model thus considered: (i) coasts as boundaries delimitating cells unselectable by the algorithm, (ii) bathymetry, (iii) a sedimentation distance where cells beyons are unselectable, (iv) river plumes as hydrodynamical fronts with an intensity and a direction (a complete circulation model in BSI is not yet available). These constraints were included in the minimal distance calculation with the transition function \(f_{j}\) used by costDistance() when creating the least-cost path, and the cutoff sedimentation threshold.

• land is set with a connectivity of 0
• bathymetry is compared between two cells:
  • when point A is shallower than point B, connectivity is high
  • when point A is deeper than point B, connectivity is low (with a certain diffusion)
• cells beyond the cutoff threshold are set with a connectivity of 0
• CDOM content (proxy of hydrodynamism) is compared between two cells (NOT IMPLEMENTED YET)

Values of the parameters used for bathymetry and hydrodynamism contraints depend on the types of particle:

• slow-sinking particles: influenced primarily by hydrodynamics and diffusing over extended areas; gravity eventually sinks them; easily resuspended
• medium-sinking particles: particles both sinking due to gravity and spreading by hydrodynamic influence, resuspension possible but difficult
• fast-sinking particles: dense aggregates that sink easily due to gravity and are unaffected by hydrodynamical effects; resuspension is highly difficult

This resulted in the following transition functions \(f_{j}\) and cutoff thresholds \(T_{k}\) (in meters):

⚠️ These values need to be groundtruthed by litterature research and expert opinion.

The equation for \(D_{ijk}\) is then:

\[ \left\{\begin{matrix} D_{ijk} = f_{k} \left( B_{i}, H_{i} \right) & D_{ij} < T_{k} \\ D_{ijk} = 0 & D_{ijk} > T_{k} \end{matrix}\right. \]

• \(f_{k}\) is the transition function
• \(B_{i}\) is the bathymetry component
• \(H_{i}\) is the hydrodynamics component
• \(T_{k}\) is the cutoff distance
• \(i\) is a cell
• \(j\) is a human activity
• \(k\) is the particle type (slow-, medium-, fast-sinking)

This allowed to calculate \(L_{ijk}\) with the inverse logarithm relationship (plus one to avoid infinite values).

\[ L^{'}_{ijk} = \frac{1}{ln(D_{ijk} + 1)} \]

\(L^{'}_{ijk}\) was standardized to vary within a scale between 0 and 1, with \(min(L^{'}_{ijk})\) and \(max(L^{'}_{ijk})\), to get \(L_{ijk}\).

Finally, the exposure index \(E_{ij}\) was computed by combining each \(L_{ijk}\) in a weighted sum using coefficients \(p_{jk}\), initialized as such:

⚠️ These values need to be groundtruthed by litterature research and expert opinion.

\[ E^{'}_{ij} = \sum_{k}^{s,m,l} \Big( L_{ijk} . p_{jk} \Big) \]

• \(L_{ijk}\) is the standardised minimal distance from the source of activity for each particle type
• \(p_{jk}\) is the proportion of each type of particle
• \(i\) is a cell
• \(j\) is a human activity
• \(k\) is the particle type (slow-, medium-, fast-sinking)

Likewise, \(E^{'}_{ij}\) was standardized to vary within a scale between 0 and 1, with \(min(E^{'}_{ij})\) and \(max(E^{'}_{ij})\), to get \(E_{ij}\).

Methodology

We extracted data from a global database for the St. Lawrence, for all fishing events occuring within the Baie des Sept-Îles. Four types of gears (traps, bottom-trawls, nets and dredges) have been considered in the bay between 2010 and 2015. Eight species have been gathered (see table at the top of this page).

As each gear was not used consistently during this period, we averaged the number of fishing events to obtain a proxy of fishing intensity. Furthermore, we modified this proxy with a smoothing function in order to ‘diffuse’ the signal around the actual event.